Related papers: Stochastic Representations for the Wave Equation o…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
A recently proposed schematic model for the non--linear rheology of dense colloidal dispersions is compared to flow curves measured in suspensions that consist of thermosensitive particles. The volume fraction of this purely repulsive model…
The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit…
This paper investigates the parabolic scaling limit of a damped stochastic wave map from the real line into the two-dimensional sphere, perturbed by multiplicative Gaussian noise of co-normal type. We prove that under this rescaling, the…
We derive a quantitative version of the hydrodynamic limit for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the $L^2$-speed of convergence of the empirical density of states in a…
We employ the tight-binding propagation method to study Klein tunneling and quantum interference in large graphene systems. With this efficient numerical scheme, we model the propagation of a wave packet through a potential barrier and…
We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and…
We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2d…
In these notes, we describe the strategy for the derivation of the hydrodynamic limit for a family of long range interacting particle systems of exclusion type with symmetric rates. For $m \in \mathbb{N}:=\{1, 2, \ldots\}$ fixed, the…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
We investigate applicability of the Hasselmann kinetic equation to the spectrum of surface gravity waves at different levels of nonlinearity in the system, which is measured as average steepness. It is shown that even in the case of…
There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical…
The flow curves, viz. the curves of stationary stress under steady shearing, are obtained close to the glass transition in dense colloidal dispersions using asymptotic expansions in a schematic model of mode coupling theory. The shear…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
The observation of fluid-like behavior in nucleus-nucleus, proton-nucleus and high-multiplicity proton-proton collisions motivates systematic studies of how different measurements approach their fluid-dynamic limit. We have developed…
Weak Wave Turbulence is a powerful theory to predict statistical observables of diverse relevant physical phenomena, such as ocean waves, magnetohydrodynamics and nonlinear optics. The theory is based upon an asymptotic closure permitted in…
Effective interface conditions for a periodically voided thin layer separating two homogeneous bulk regions are derived for the elastic wave equation by taking the simultaneous limit of vanishing layer periodicity and layer thickness. The…
A kinetic model for the elasto-plastic dynamics of a flowing jammed material is proposed, which takes the form of a non-local -- Boltzmann-like -- kinetic equation for the stress distribution function. Coarse-graining this equation yields a…
We study experimentally blast wave dynamics on a weakly interacting fluid of light. The fluid density and velocity are measured in 1D and 2D geometries. Using a state equation arising from the analogy between optical propagation in the…